### Abstract

In this work, we explicitly show the existence of two frequency regimes in a two-dimensional Hindmarsh–Rose neural network. Each of the regimes, through the semi-discrete approximation, is shown to be described by a two-dimensional complex Ginzburg–Landau equation. The modulational instability phenomenon for the two regimes is studied, with consideration given to the coupling intensities among neighboring neurons. Analytical solutions are also investigated, along with their propagation in the two frequency regimes. These waves, depending on the coupling strength, are identified as breathers, impulses and trains of soliton-like structures. Although the waves in two regimes appear in some common regions of parameters, some phase differences are noticed and the global dynamics of the system is highly influenced by the values of the coupling terms. For some values of such parameters, the high-frequency regime displays modulated trains of waves, while the low-frequency dynamics keeps the original asymmetric character of action potentials. We argue that in a wide range of pathological situations, strong interactions among neurons can be responsible for some pathological states, including schizophrenia and epilepsy.

Original language | English |
---|---|

Pages (from-to) | 186-198 |

Number of pages | 13 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 474 |

DOIs | |

Publication status | Published - May 15 2017 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physica A: Statistical Mechanics and its Applications*,

*474*, 186-198. https://doi.org/10.1016/j.physa.2017.01.075

}

*Physica A: Statistical Mechanics and its Applications*, vol. 474, pp. 186-198. https://doi.org/10.1016/j.physa.2017.01.075

**Frequency mode excitations in two-dimensional Hindmarsh–Rose neural networks.** / Tabi, Conrad Bertrand; Etémé, Armand Sylvin; Mohamadou, Alidou.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Frequency mode excitations in two-dimensional Hindmarsh–Rose neural networks

AU - Tabi, Conrad Bertrand

AU - Etémé, Armand Sylvin

AU - Mohamadou, Alidou

PY - 2017/5/15

Y1 - 2017/5/15

N2 - In this work, we explicitly show the existence of two frequency regimes in a two-dimensional Hindmarsh–Rose neural network. Each of the regimes, through the semi-discrete approximation, is shown to be described by a two-dimensional complex Ginzburg–Landau equation. The modulational instability phenomenon for the two regimes is studied, with consideration given to the coupling intensities among neighboring neurons. Analytical solutions are also investigated, along with their propagation in the two frequency regimes. These waves, depending on the coupling strength, are identified as breathers, impulses and trains of soliton-like structures. Although the waves in two regimes appear in some common regions of parameters, some phase differences are noticed and the global dynamics of the system is highly influenced by the values of the coupling terms. For some values of such parameters, the high-frequency regime displays modulated trains of waves, while the low-frequency dynamics keeps the original asymmetric character of action potentials. We argue that in a wide range of pathological situations, strong interactions among neurons can be responsible for some pathological states, including schizophrenia and epilepsy.

AB - In this work, we explicitly show the existence of two frequency regimes in a two-dimensional Hindmarsh–Rose neural network. Each of the regimes, through the semi-discrete approximation, is shown to be described by a two-dimensional complex Ginzburg–Landau equation. The modulational instability phenomenon for the two regimes is studied, with consideration given to the coupling intensities among neighboring neurons. Analytical solutions are also investigated, along with their propagation in the two frequency regimes. These waves, depending on the coupling strength, are identified as breathers, impulses and trains of soliton-like structures. Although the waves in two regimes appear in some common regions of parameters, some phase differences are noticed and the global dynamics of the system is highly influenced by the values of the coupling terms. For some values of such parameters, the high-frequency regime displays modulated trains of waves, while the low-frequency dynamics keeps the original asymmetric character of action potentials. We argue that in a wide range of pathological situations, strong interactions among neurons can be responsible for some pathological states, including schizophrenia and epilepsy.

UR - http://www.scopus.com/inward/record.url?scp=85010899697&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85010899697&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2017.01.075

DO - 10.1016/j.physa.2017.01.075

M3 - Article

AN - SCOPUS:85010899697

VL - 474

SP - 186

EP - 198

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

ER -